Since the 1970s, calculators have a very simple computer inside of it, which runs a simple program for doing math. They are very slow (kilohertz) and have very little memory (bytes).
Scientific calculators are a bit more complicated, so they require slightly more powerful processors and more memory. The processing power is still miniscule compared to any kind of normal computer.
Lastly graphing calculators are arguably real computers. Depending on the model, they pack power comparable to a full size computer or even workstation from the 1980s or 1990s. They can often run 3rd party programs which can be downloaded by serial cable, usb, or even wirelessly on some models. The main thing holding graphing calculators back is that they are usually designed to comply with the rules for standardized tests, which limit the amount of functionality they are allowed to have.
For instance, the TI-84 uses a Z80 processor, which is similar (but faster) than the ones used in the Tandy TRS-80 home computer or the Nintendo Gameboy. The TI-89 uses a Motorola 68000 processor, which was used in high-end Unix workstations in the early 1980s, as well as being used in the Sega Genesis. Some of the new TI nSpire calculators use ARM processors running at hundreds of megahertz, which probably compare favorably to a Pentium II or Pentium III computer from the 1990s.
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